拓扑空间在自映射下的不动点问题是经典且富有内涵的课题，它与几何群论也有紧密的联系。图（有限一维复形）及曲面自映射的不动点类指数及不动子群秩的关系已经清楚，其不动子群秩的界也已给出。本项目拟对三维可几何化流形及Haken流形自同胚的不动点及不动子群进行研究。

Fixed point theory is a significant topic in topology,and is closely related to geometric group theory. For selfmaps of hyperbolic surfaces and graphs, some bounds involving the rank and the index of fixed point classes were given. One consequence was a rank bound for fixed subgroups of surface group endomorphisms, similar to the Bestvina-Handel bound (originally known as the Scott conjecture) for free group automorphisms. We will study the fixed points and the fixed subgproups of self-homeomorphisms of closed orientable 3-manifolds which are either Haken or geometric in this program.